Multiple Integration on Time Scales

Böhner, Martin; Georgiev, Svetlin G.

doi:10.1007/978-3-319-47620-9_7

Cited by 45 publications

(43 citation statements)

References 4 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…The inequalities will be proved for several variables and based on the definitions of the multiple Riemann and Lebesgue Δ-integration on time scales given in [53].…”

Section: This Inequality Is Reversed Ifmentioning

confidence: 99%

Dynamic Inequalities On Time Scales

Agarwal¹,

O’Regan²,

Saker³

2014

154

View full text Add to dashboard Cite

“…The inequalities will be proved for several variables and based on the definitions of the multiple Riemann and Lebesgue Δ-integration on time scales given in [53].…”

Section: This Inequality Is Reversed Ifmentioning

confidence: 99%

Dynamic Inequalities On Time Scales

Agarwal¹,

O’Regan²,

Saker³

2014

154

View full text Add to dashboard Cite

“…On the last line, we first used the Riemann-type definition of the k-dimensional integral on time scales (see [4]), then Fubini's theorem, and finally the definition of the time scale polynomials. Note that a multidimensional integral on the product of time scales is just the ordinary Lebesgue integral with respect to a suitable measure (see [5]), and hence the use of Fubini's theorem is justified.…”

Section: Preliminariesmentioning

confidence: 99%

Dynamic diffusion-type equations on discrete-space domains

Slavík

Stehlı́k

2015

Journal of Mathematical Analysis and Applications

View full text Add to dashboard Cite

We consider a class of partial dynamic equations on discrete-space domains which includes, as a special case, the discrete-space versions of the diffusion (heat) equation. We focus on initial-value problems and study the existence and uniqueness of forward and backward solutions. Moreover, we discuss other topics such as sum and sign preservation, maximum and minimum principles, or symmetry of solutions.

show abstract

“…2 σ (t)+4 + σ (t)− 9 16−(σ (t)) 2 − σ (t)−3 (σ (t)) 2 −8σ (t) +16 , σ (t) / ∈ {−4, 4}, 4. 2ρ(t)−1 2ρ(t) − 1 2ρ(t)−4(ρ(t)) 2 − 2ρ(t) 2ρ(t)−1 , ρ(t) / ∈ − 1 2 , 0, 1 2 , 5.…”

Section: Exercise 122 For T ∈ T Simplifyunclassified

“…In [9], the Darboux and Riemann definitions of multiple integrals on time scales over arbitrary regions for functions of two variables are introduced. As before, this chapter considers only delta integrals.…”

Section: Notes and Referencesmentioning

confidence: 99%